7x^2+23x-17=13-6x

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Solution for 7x^2+23x-17=13-6x equation: 


Simplifying
7x2 + 23x + -17 = 13 + -6x

Reorder the terms:
-17 + 23x + 7x2 = 13 + -6x

Solving
-17 + 23x + 7x2 = 13 + -6x

Solving for variable 'x'.

Reorder the terms:
-17 + -13 + 23x + 6x + 7x2 = 13 + -6x + -13 + 6x

Combine like terms: -17 + -13 = -30
-30 + 23x + 6x + 7x2 = 13 + -6x + -13 + 6x

Combine like terms: 23x + 6x = 29x
-30 + 29x + 7x2 = 13 + -6x + -13 + 6x

Reorder the terms:
-30 + 29x + 7x2 = 13 + -13 + -6x + 6x

Combine like terms: 13 + -13 = 0
-30 + 29x + 7x2 = 0 + -6x + 6x
-30 + 29x + 7x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-30 + 29x + 7x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -7x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {-5, 0.8571428571}

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